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- Title
Large deviation principle in one-dimensional dynamics.
- Authors
Chung, Yong Moo; Rivera-Letelier, Juan; Takahasi, Hiroki
- Abstract
We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.
- Subjects
LARGE deviations (Mathematics)
- Publication
Inventiones Mathematicae, 2019, Vol 218, Issue 3, p853
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-019-00899-w